FRELINGHUYSEN MIDDLE SCHOOL

 

COURSE PROFICIENCIES

 

 

COURSE:  ALGEBRA                                                                                                         GRADE 8

 

I.          COURSE OVERVIEW:

 

            The purpose of this course is to introduce students to the concepts of algebra in a college preparatory program.  The scope of the course is to expand the students’ mathematical knowledge through a variety of activities that include reasoning, problem-solving and communication.

 

II.        PROFICIENCIES:  (Specific measurable student outcomes written in behavioral terms to include one or more of the following:  Skills, Knowledge, Attitudes and Behavior.)

 

            Upon the successful completion of this course, the students will:

 

             1.        Understand sets and set notation.

             2.        Be able to simplify expressions involving more than one operation.

             3.        Be able to substitute values for variables in order to evaluate algebraic expressions.

             4.        Comprehend the mechanics of simplifying expressions, including those containing

one or more enclosures.

             5.        Be able to identify the properties of integers, including negative numbers,

and perform accurately the basic operations involving them.

                        accurately the basic operations involving them.

             6.        Solve several types of equations including simple systems of linear, those

containing fractions and/or enclosures as well as quadratics.

             7.        Show proficiency in writing English phrases in mathematical terms and be able

to solve word problems of many types.

             8.        Be able to simplify products and powers and evaluate algebraic expressions

                        containing them.

             9.        Demonstrate how to perform the four basic operations on polynomials, including the

                        multiplication at sight of certain special products.

            10.       Show mastery of factoring skills and be able to identify the need for them in specific

                        algebraic situations.

            11.       Show mastery in solving algebraic fractions.

            12.       Demonstrate an understanding of Cartesian coordinates and their use in graphing a

straight line and solving systems of linear equations graphically.

            13.       Be able to obtain and use the slope of a line and write the equation of a line given

                        certain conditions.

            14.       Use the study skills required to enhance his/her learning, retention, and application

of mathematical skills effectively.

            15.       Appropriately integrate technology with the curriculum.

            16.       Improve his/her understanding of the relationship between mathematics education

and career choice.

 

FRELINGHUYSEN MIDDLE SCHOOL

 

COURSE PROFICIENCIES

 

 

COURSES:                ADVANCED ALGEBRA AND CONNECTED MATHEMATICS

 

 

METHODS OF EVALUATION:

 

            1.         Homework

            2.         Tests

            3.         Quizzes

            4.         Notebook

            5.         Class Participation

 

 

MATERIALS NEEDED FOR CLASS:

 

            1.         Textbook

            2.         Loose-leaf binder with 5 dividers

            3.         Pencils, erasers, hi-liters

            4.         Optional:  scientific calculator, ruler, protractor, compass

 

 

CRITERIA FOR EXCELLENCE:  (Requirements for achieving an “A” in this course.)

 

            1.         Homework, tests, quizzes and notebooks must average between 90 – 100

            2.         Class participation and effort are important factors

 

 

MAKE-UP AND EXTRA HELP POLICIES:

 

            1.         A student who is absent must make up and correct all missed work

            2.         Student and teacher will conference regarding an appropriate due date

            3.         Students may submit work late, BUT they cannot receive full credit since that would

not be fair

4.         Extra help is provided before school by appointment or during 9th period

 

 

 

 

FRELINGHUSYEN MIDDLE SCHOOL

 

COURSE PROFICIENCIES

 

 

COURSE:       CONNECTED MATHEMATICS                                                                GRADE 8

 

I.                      COURSE OVERVIEW:

 

                        In designing a complete and connected middle school mathematics curriculum, it is not possible to separate the influence of what is taught from how it is taught.  What students learn from the curriculum, i.e., the mathematical content of the curriculum is shaped by how they learn to work with mathematics, i.e. the mathematical processes imbedded in the curriculum.  Conversely, how students learn to use mathematics shapes, what they learn about mathematics, and how concepts are understood and related.

 

II.        CONTENT GOALS:

 

                        NUMBER:  Number sense and reasoning with and about numbers; number theory;

properties and operations of number systems, with focus on integers and rational

numbers; number estimation; ratio, proportion, and percentage; representation of

numbers in concrete, graphic and symbolic forms; scientific notation; and exponential

notation

 

                        GEOMETRY:  Spatial sense and reasoning with and about shapes and location;

two- and three-dimensional shapes and their properties; relations among shapes

(congruence, similarity, parallelism, perpendicularity, symmetry): location; coordinate

systems; transformations, visualization, and sketching of shapes

 

                        MEASUREMENT:  A sense of what it means to measure and to reason with

measures; concepts of length, area, volume, mass, angle measure; common

properties  of measurement systems; procedures for exact, approximate and

derived measurements; estimation

 

                        ALGEBRA:  Algebraic reasoning; variables, patterns and functions, relations;

modeling; representation by symbolic expressions, numerical tables and graphs;

equations and inequalities; and rates of change

 

                        STATISTICS:  Decision-making with data; formulating questions, collecting,

displaying, analyzing, making inferences from data; and sampling

 

                        PROBABILITY:  Decision-making under uncertainty; random events; equally

likely events and unequally likely events; experimental and theoretical probability;

expected value; simulation

 

 

                                    The four overarching goals in the National Council of Teachers in Mathematics

                                    Curriculum and Evaluation Standards for School Mathematics serve as the major

                                    process goals for this course.

 

III.       SPECIFIC CONTENT:

                        Moving Straight Ahead

·        Further develop the understanding of variables and patterns

·        Identify variables

·        Determine an appropriate range of values for independent and dependent variables

·        Collect data, use in tables, make predictions

·        Use graphing calculators to investigate linear relationships

·        Recognize linear relationships in all forms of representation: written descriptions, tables, graphs, symbols

·        Recognize a change and its effect on various representations: change the slope; change the y-intercept

·        Solve a linear function of the form y = mx + b using different methods:  tables, graphs, equations

·        Given certain information, find the slope and the y-intercept

·        Write a linear equation and interpret its meaning

·        Find a solution common to two linear equations by graphing or creating tables

 

Filling and Wrapping

·        Conceptualize volume and surface area:  volume as a measure of filling an object; surface area as a measure of wrapping an object

·        Develop the concept of volume and surface area of prisms, cylinders, cones, spheres

·        Investigate the effects of varying dimensions on the volume and surface area

·        Estimate the volume of an irregular shape by measuring the amount of water displaced

 

Kaleidoscopes, Hubcaps and Mirrors

·        Explore symmetry:  understand important properties; recognize and describe symmetries of figures; use tools to examine symmetry and transformations; create figures with specified symmetries; perform symmetry transformations, including reflections, translations, rotations; find symmetries of geometric figures

·        Identify basic elements that can be used to replicate a given design

·        Give precise mathematical directions for performing transformations

·        Write coordinate rules for specifying the image of a general point (x, y)

·        Combine transformations and find a single transformation to get the same result

·        Appreciate the power of transformational geometry to describe motions, patterns and designs in the real world

 

Samples and Populations

·        Employ the process of statistical investigation to explore problems

·        Analyze data using:  tables, histograms, stem-and-leaf plots; box-and-whiskers plots

·        Compare data using: measures of central tendency (mean, median); measures of spread (range, percentile); data displays

·        Explore data using scatter plots

·        Distinguish between samples and populations, compare samples

·        Infer conclusions about the population based on sample data

·        Understand the concept of randomness and select random samples

·        Design a survey

 

Clever Counting

·        Recognize situations in which counting techniques apply

·        Construct organized lists of outcomes

·        Analyze counting problems involving choices

·        Differentiate among situations:  Does order matter?  Are repeats allowed?

·        Explore networks:  analyze the number of paths; compare the structures with problems involving combinations; create networks with given constraints

 

 

 

 

FRELINGHUYSEN MIDDLE SCHOOL

 

COURSE STANDARDS

 

 

COURSE:       MATHEMATICS                                                                                          GRADE 8

 

 

METHODS OF EVALUATION:

 

            1.         Quizzes

            2.         Tests

            3.         Homework

            4.         Class Participation

            5.         Notebook

 

 

MATERIALS NEEDED FOR CLASS:

 

            1.         Textbook

            2.         Loose-leaf notebook

            3.         Pencil/Pen

            r.          Optional:  calculator, ruler, compass, protractor

 

 

CRITERIA FOR EXCELLENCE:  (Requirements for receiving an “A” in this course.)

 

            1.         Homework, quizzes, tests and notebooks must average between 90 – 100

            2.         Homework, class participation and effort are important factors

 

 

MAKE-UP AND EXTRA HELP POLICIES:

 

1.         A student who is absent must make up all missed work.  Student and teacher will conference regarding an appropriate due date

2.         Students may submit work late, but they cannot receive full credit since that would not be fair

            3.         Extra help is provided before or after school by appointment